Non-convex block-sparse compressed sensing with redundant dictionaries

What is it about?

Under the Block D-RIP condition , a sufficient condition for robust signal reconstruction with redundant dictionaries by mixed l2/lp(0< p<1) minimization is established. Furthermore, our theoretical results show that,the block k-sparse signal can be stably reconstructed via nonconvex l2/lp minimization with redundant dictionaries in the presence of noise. Particularly, this improves the existed result when the block-sparse signal degenerate to the conventional signal case. Besides, we also obtain robust reconstruction condition and error upper bound estimation when the block number is no more than four times the sparsity of the block signal (d<=4k).And the numerical experiments to some extent testify the performance of nonconvex l2/lp(0< p<1) minimization with redundant dictionaries.

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Why is it important?

we also further investigate the block-sparse compressed sensing with redundant dictionary by using Block D-RIP and Block D-ROP. Nowadays, there are few works with redundant dictionaries by mixed l2/lp(0< p<1) minimization. By the fast developments of information technology, people usually need to face with different huge high-dimensional massive datasets, and thus it is important to investigate nonconvex block-sparse compressed sensing with redundant dictionaries in signal processing.